A spacecraft attitude control system and method in which an attitude controller is configured for sensing three-dimensional attitude of the spacecraft, and producing torque signals for stabilizing the spacecraft in a prescribed attitude in space. At least four mutually skew reaction wheels are rotated in response to the torque control signals for storing three-dimensional angular momentum, and speeds of rotation of the wheels are measured. A reaction wheel speed control processor, responsive to reaction wheel torque and speed for producing reaction wheel spin control signals, implements an infinity-norm algorithm for causing the nullspace components of wheel speed to re-distribute a desired three-dimensional stabilizing momentum of the spacecraft in such a manner that the maximum speeds of rotation of all the reaction wheels is minimized. As a result, periods between successive momentum dumping maneuvers are prolonged to the maximum possible.